Respuesta :
Answer:
The value of the quantity after 186 hours is 2089.41
Step-by-step explanation:
We can use exponential formula
[tex]P(t)=a(1-b)^{\frac{t}{h} }[/tex]
a quantity with an initial value of 2100
so,
[tex]a=2100[/tex]
decays exponentially at a rate of 0.65% every 10 days
So, b=0.0065 when h=10*24=240
now, we can plug values
[tex]P(t)=2100(1-0.0065)^{\frac{t}{240} }[/tex]
now, we can plug t=186
and we get
[tex]P(186)=2100(1-0.0065)^{\frac{186}{240} }[/tex]
[tex]=2089.413[/tex]
Answer:
Q(186) = 2089.463
Step-by-step explanation:
Formula for decaying exponentially:
Q(t) = Q_0 e^{-rt}
where, Q(t)= quantity at time t
Q_0 = initial quantity value (2100)
t = time (186 hours)
r = rate of decaying (0.65)
r = 0.65% = 10 days
1 day = [tex]\frac{0.0065}{10}[/tex]
1 hour = [tex]\frac{0.0065}{240}[/tex]
186 hours = [tex]\frac{0.0065*186}{240}[/tex]
rt = 0.00503
Q(186) = 2100*e^{-0.00503}
= 2089.46
